A277734 -id:A277734 - cp's OEIS frontend

A277731 Fixed point of the morphism 0 -> 01, 1 -> 012, 2 -> 0; starting with a(1) = 0.

0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 2, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 2

Offset: 1

N. J. A. Sloane, Nov 07 2016

nonn

After k = 0,1,2,3,... applications of the morphism we have 0, 01, 01012, 01012010120, ... which have lengths 1, 2, 5, 11, 24, 53, 117, ..., satisfying b(n) = 2*b(n-1) + b(n-3) (cf. A052980).

N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Cf. A052980, A277732, A277733, A277734.

with(ListTools);
T:=proc(S) Flatten(subs( {0=[0,1], 1=[0,1,2], 2=[0]}, S)); end;
S:=[0];
for n from 1 to 10 do S:=T(S); od:
S;

m = 100; (* number of terms required *)
S[1] = {0};
S[n_] := S[n] = SubstitutionSystem[{0 -> {0, 1}, 1 -> {0, 1, 2}, 2 -> {0}}, S[n-1]];
For[n = 2, True, n++, If[PadRight[S[n], m] == PadRight[S[n-1], m], Print["n = ", n]; Break[]]];
Take[S[n], m] (* Jean-François Alcover, Mar 20 2023 *)

A277732 Positions of 0's in A277731.

Original entry on oeis.org

1, 3, 6, 8, 11, 12, 14, 17, 19, 22, 23, 25, 27, 30, 32, 35, 36, 38, 41, 43, 46, 47, 49, 51, 54, 56, 59, 61, 64, 65, 67, 70, 72, 75, 76, 78, 80, 83, 85, 88, 89, 91, 94, 96, 99, 100, 102, 104, 107, 109, 112, 114, 117, 118, 120, 123, 125, 128, 129, 131, 134, 136, 139, 140, 142, 144, 147, 149, 152, 153

Offset: 1

N. J. A. Sloane, Nov 07 2016

nonn

{A277732, A277733, A277734} forms a three-way partition of the positive integers, similar to {A003144, A003145, A003146}.

N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Cf. A052980, A277731, A277733, A277734.

Cf. also A003144, A003145, A003146.

with(ListTools);
T:=proc(S) Flatten(subs( {0=[0,1], 1=[0,1,2], 2=[0]}, S)); end;
S:=[0];
for n from 1 to 14 do S:=T(S); od:
S; # A277731
p0:=[]: p1:=[]: p2:=[]:
for i from 1 to nops(S) do
j:=S[i];
if j=0 then p0:=[op(p0),i];
elif j=1 then p1:=[op(p1),i];
else p2:=[op(p2),i]; fi: od:
p0; # A277732
p1; # A277733
p2; # A277734

m = 1000; (* number of terms of A277731 *)
S[1] = {0};
S[n_] := S[n] = SubstitutionSystem[{0 -> {0, 1}, 1 -> {0, 1, 2}, 2 -> {0}}, S[n - 1]];
For[n = 2, True, n++, If[PadRight[S[n], m] == PadRight[S[n - 1], m], Print["n = ", n]; Break[]]];
A277731 = Take[S[n], m];
Position[A277731, 0] // Flatten (* Jean-François Alcover, Mar 20 2023 *)

A277733 Positions of 1's in A277731.

Original entry on oeis.org

2, 4, 7, 9, 13, 15, 18, 20, 24, 26, 28, 31, 33, 37, 39, 42, 44, 48, 50, 52, 55, 57, 60, 62, 66, 68, 71, 73, 77, 79, 81, 84, 86, 90, 92, 95, 97, 101, 103, 105, 108, 110, 113, 115, 119, 121, 124, 126, 130, 132, 135, 137, 141, 143, 145, 148, 150, 154, 156, 159, 161, 165, 167, 169, 172, 174, 177, 179

Offset: 1

N. J. A. Sloane, Nov 07 2016

nonn

{A277732, A277733, A277734} forms a three-way partition of the positive integers, similar to {A003144, A003145, A003146}.

N. J. A. Sloane, Table of n, a(n) for n = 1..20000

Cf. A052980, A277731, A277732, A277734.

Cf. also A003144, A003145, A003146.

Maple
```
See A277732.
```

m = 1000; (* number of terms of A277731 *)
S[1] = {0};
S[n_] := S[n] = SubstitutionSystem[{0 -> {0, 1}, 1 -> {0, 1, 2}, 2 -> {0}}, S[n - 1]];
For[n = 2, True, n++, If[PadRight[S[n], m] == PadRight[S[n - 1], m], Print["n = ", n]; Break[]]];
A277731 = Take[S[n], m];
Position[A277731, 1] // Flatten (* Jean-François Alcover, Mar 20 2023 *)

cp's OEIS Frontend

A277731 Fixed point of the morphism 0 -> 01, 1 -> 012, 2 -> 0; starting with a(1) = 0.

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A277732 Positions of 0's in A277731.

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A277733 Positions of 1's in A277731.

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